President Trump said the US would "grieve and pray" for the victims, but added states that "sponsor terrorism risk falling victim to the evil they promote."
Iran has denounced as "repugnant" US President Donald Trump's reaction to Wednesday's deadly attacks in Tehran.
Iran's foreign minister Mohammad Javad Zarif on Thursday rejected Trump's condolences for the twin attacks in the capital.
Repugnant WH statement & Senate sanctions as Iranians counter terror backed by US clients.Iranian people reject such US claims of friendship— Javad Zarif (@JZarif) June 8, 2017
Trump had said he prayed for the victims of the attacks claimed by Daesh, but added that "states that sponsor terrorism risk falling victim to the evil they promote."
The Trump administration issues a statement essentially blaming Iran for the terrorist attack against Iranians: pic.twitter.com/rYVxyfBSle— Daniel Dale (@ddale8) June 7, 2017
The attacks on Tehran's parliamentary complex and the shrine of revolutionary leader Ayatollah Ruhollah Khomeini killed at least 17 people and wounded more than 40 on Wednesday.
They were the first claimed by Daesh in Iran.
Deputy Secretary of Iran's Supreme National Security Council Reza Seifollahi said five of the attackers who died in the assault were Iranians who had joined Daesh.
They were armed with rifles and pistols and at least two blew themselves up with suicide vests, Iranian media reported.
"They earlier left Iran and were involved in the crimes of the terrorist group in Raqqa and Mosul," the ministry said, referring to Daesh's de-facto capital in Syria and a city it captured in Iraq.
"Last year, they returned to Iran ... to carry out terrorist attacks in the holy cities of Iran," the ministry added in a statement on state news agency IRNA.
Police say five people were arrested around Khomeini's shrine on suspicion of involvement, while the intelligence ministry said a third team had been stopped before the attacks started.
Iran's intelligence ministry said earlier on Thursday it had arrested more suspects linked to the attacks, in addition to six Iranians, including one woman, detained on Wednesday.
Daesh targets Iran
Daesh has threatened to step up recruitment within Iran, releasing its first Persian-language video in March in which it threatened to "conquer Iran and restore it to the Sunni Muslim nation as it was before."
Daesh considers predominantly Shia Iran to be apostates, and Tehran is deeply involved in fighting the group in Syria and Iraq.
Iran has a sizeable Sunni population along its restive borders with Iraq and Pakistan from which Daesh is hoping to recruit.
Trump's comments were criticised by Iranians on social media. They contrasted Trump's words with Tehran's offer of support and candlelight vigils in Iran after the attacks of September 11, 2001, on the United States.
Attacks in Iran were part of a bigger picture
The US president has long accused Iran of backing terrorism and has threatened to tear up a 2015 nuclear deal between Tehran and major powers.
Even as Washington expressed its condolences on Wednesday, the US Senate advanced legislation that would impose new sanctions on Iran, partly for what the bill described as the Iranian regime's "support for acts of international terrorism."
However, Iranian security officials counter that it is their regional rival Saudi Arabia, a close US ally, that is responsible for funding and spreading the extremism that underpins Daesh.
Iran's Revolutionary Guards accused Riyadh and Washington of being "involved" in Wednesday's attacks, drawing a link to Trump's recent visit to Saudi Arabia.
"For these two actions to happen ... after this meeting means that the US and Saudi regimes had ordered their stooges to do this," said Mohammad Hossein Nejat, deputy head of the Revolutionary Guards intelligence branch, according to the Fars news agency.
Other Iranian leaders sought to play down the attacks, with Supreme Leader Ayatollah Ali Khamenei saying: "These firecrackers that happened today will not have the slightest effect on the will of the people."
Parliament was in session as the violence unfolded and members were keen to show they were undeterred, continuing with regular business.
President Hassan Rouhani said, "Terrorism is a global problem, and unity to fight extremism, violence and terrorism with regional and international cooperation is the most important need of today's world."